I hate to say it but some men are just that way in my experience. The dog sounds fine with you keeping an eye on it and is probably the only thing your dad opens up to so I’d say leave the dog with him, it’s his dog, it’s walked and cared for and quite frankly it’s your dads only real company and his companion when you’re not there. He sounds a bit depressed, which is quite natural as he’s lost your mum. Look at it from his point of view, he’d probably had his ‘mate’ for decades before she passed away and although at the beginning of his grief would of felt lost and alone it’s something he’s had to just learn to live with and his way of life has probably become a habit to him now, again in my experience from dealing with 5 parents (inc a step parent) the older they get the more habitual they will become! My father in law sounded like your dad, wouldn’t let anyone do anything in or outside the property, had his habits etc and stuck to them rigidly and just sat in front of the TV all day sleeping for much of it but we now realised he had dementia at the end because he kept my mother in law awake at night talking and walking about until he got nasty and we had to have him sectioned. But we never put 2 and 2 together until his death. My DH has now got vascular dementia and that is how he started off, dropping off to sleep mainly at night then hallucinating dreams he started acting out. Maybe this is happening to your dad? But he wouldn’t know it’s happening, my husband denied it for a couple of years until he saw the state I was getting into with no sleep and illness he was causing. During the day for the first couple of years you wouldn’t of really known there was anything wrong with him apart from DH kept falling asleep in the chair half the day.
Your dad is 86, still independent and as much as it might annoy you the way he lives I’d just say keep an eye on the situation and his dog obviously but let him get on with his life if that’s the way he’s chosen to live now. He won’t change if it’s his choice as much as you want him too, so don’t stress yourself or him up by trying to force him it’s honestly not worth it, you don’t know what goes through his mind if he’s happy to live in his own little way and let’s face it none of us know how much we will want to just sit on our backsides in later life, it’s his choice to do as he pleases. One last thing, are his iron and Vit D levels up as that can cause not only tiredness but depression especially in the elderly.